• East Asian mathematical journal
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• v.32 no.4
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• pp.443-464
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• 2016

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students' mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.

• School Mathematics
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• v.11 no.4
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• pp.745-771
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• 2009

To acquire the hints of the development of children's multiplication strategies, this study tried to find the differences between the students who learned multiplication and the students who didn't. And we also tried to explore their acquired computational resources. As a result, we confirm that there is a certain direction on the development of children's multiplication strategies according to their grades and the level of acquirement of mathematical knowledge. Moreover, we comprehend that commutative law is an important part of the strategies on two-digit multiplication and that acquisition of the computational resources must precede the learning of multiplication strategies. In the end part, this article proposes a new taxonomy of strategies for multiplication. To support our proposal, we integrated the prior researches with our findings.

• School Mathematics
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• v.15 no.4
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• pp.889-920
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• 2013

The aim of this study is to look into the didactical background for introducing the concept of multiplication and teaching multiplication facts in elementary school mathematics and offer suggestions to improve teaching multiplication in the future. In order to attain these purposes, this study deduced and examined concepts of multiplication, situations involving multiplication, didactical models for multiplication and multiplication strategies based on key ideas with respect to the didactical background on teaching multiplication through a theoretical consideration regarding various studies on multiplication. Based on such examination, this study compared and analyzed textbooks used in the United States, Finland, the Netherlands, Germany and South Korea. In the light of such theoretical consideration and analytical results, this study provided implication for improving teaching multiplication in elementary schools in Korea as follows: diversifying equal groups situations, emphasizing multiplicative comparison situations, reconsidering Cartesian product situations for providing situations involving multiplication, balancing among the group model, array model and line model and transposing from material models to structured and formal ones in using didactical models for multiplication, emphasizing multiplication strategies and properties of multiplication and connecting learned facts and new facts with one another for teaching multiplication facts.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.155-171
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• 2007

One second grader, Junsu, was observed 4 times before and after formal multiplication lesson in Grade 2. This study describes how solution strategies in multiplication problems develop over time and investigates awareness of the relation between situation and computation in simple measurement and partitive division problems as informally experienced. It was found that Junsu used additive calculation for small-number multiplication problems but could not solve large-number multiplication problems and that he did not have concept of mathematical terms at first interview stage. After formal teaching, Junsu learned a variety of multiplication solution strategies and transferred from additive calculation to multiplicative calculation. The cognitive processing load of each strategy was gradually reduced. Junsu experienced measurement division as a dealing strategy and partitive division as a estimate-adjust strategy dealing more than one object in the first round.

• East Asian mathematical journal
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• v.33 no.4
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• pp.353-380
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• 2017

The purpose of this study is to analyze the multiplication units in the elementary school mathematics. In the 2015 revised curriculum, students learn multiplication in $2^{nd}$ grade. The multiplication units is divided into two: multiplication and multiplication facts. In these two units, we mainly analyze situations involving multiplication, models for teaching multiplication, and multiplication strategies for teaching multiplication facts in relation to Subject Matter Knowledge. We called these contents Multiplication Matter Knowledge. We examined the precedent study with regard to multiplication at the elementary mathematics. As results, we prepared an analysis framework for this study. This study was conducted according to qualitative research methods, expecially 'qualitative contents analysis'. The contents here refer to Multiplication Matter Knowledge that can be found in the elementary mathematics textbooks and working books etc. As results of analysis, We can confirm that various multiplication situations and multiplication models are presented in the textbooks. And it has been examined that various multiplication properties are presented in the textbook according to the multiplication strategy levels. We insist elementary school teachers should be aware of these Multiplication Matter Knowledge. This study aims to provide elementary school teachers with basic data in these contexts.

• The Mathematical Education
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• v.47 no.4
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• pp.405-419
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• 2008

The purpose of this study is to find oui the effects of teaching mathematical concepts by designing and applying teaching and learning programs that takes into consideration the students' strong intelligence, through the teaching and learning strategies based on the multiple intelligences theory. For this study, developmental and experimental research was conducted. In the developmental research part of the study, teaching and learning programs for teaching the concept of multiplication were designed and the activities based on the multiple intelligences were chosen. On the other hand, in the experimental research part, the data acquired from the application of nonequivalent control group pretest-posttest design in the actual classes was processed and analyzed. The results above indicate that the teaching and learning program based on the multiple intelligences theory improved the students' overall understanding of mathematical concepts by providing various types of activities. In addition, this program helped students to increase their confidence and generate a positive attitude towards learning math.

• The Mathematical Education
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• v.50 no.3
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• pp.337-354
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• 2011

The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students' understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

• East Asian mathematical journal
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• v.36 no.2
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• pp.253-271
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• 2020

The purpose of this study was to see the effects of a learning method of the multiplication play activities on improving the mathematical thinking ability and mathematical attitude of 2nd grade students in elementary school. We chose 19 students of the 2nd grade experimental group of D elementary school in the D city to conduct this research. The result of this study are as follows. First, Classes using multiplicative play activities have a positive effect on students' mathematical thinking ability. When analyzing transcripts and activities, students were able to think of strategies that could solve the problem according to the situation. Second, Classes using multiplicative play activities, in result of this they have positive effect mathematical attitude than using textbook in terms of attitude about mathematical subject and habits of study. In conclusion, the multiplication play activities are effective to improve mathematical thinking ability and attitude of second elementary school students. It can be a implication for the method of improving mathematical thinking ability and attitude.

• School Mathematics
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• v.9 no.4
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• pp.507-521
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• 2007

The purpose of this study was to investigate the effects of memory retention of mathematical concepts in multiplication in the inquiry-based pantomime instructions. Three months later after the pre-test, a comparison was made between traditional class (TC) and class with the inquiry-based pantomime (IP) approach in terms of students retention of mathematical understandings. Results of the study indicated that the If instructions promoted effective long-term retention of knowledge. We concluded that instructional strategies that promoted active engagement in learning using life examples and drawings produced effective long-term retention of knowledge.

• Research in Mathematical Education
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• v.15 no.2
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• pp.197-208
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• 2011

By using the recording and quantitative analysis of two videos about "The multiplication and division of the Fractions" and the "Flanders Interaction Analysis System," we classified the teachers' language of instruction in algebra classroom and also analysis the language of instruction in the different teaching process. The results after the analysis as follows: (1) The proportion of time was taken in teachers' language of instruction is high and vary in types, most of the teachers' language is teachers' question; (2) In the different teaching process, the proportion of time was taken in teachers' language of instruction is different; (3) Teachers attached importance to explain the example and had the similar teaching strategy, but the teachers' language is different; (4) In the practice process, teachers placed importance on exploring the tough question and its teaching strategies are different. The teachers' questions are the main teachers' language of instruction.